Finite Group Databasebeta

← #14739016

Subgroups — #14739016

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079763C211yesmaximal, characteristic, complemented
2#13078408C211yesmaximal, characteristic
3D11×#476C211yesmaximal, characteristic
4#13077637C211yesmaximal, characteristic
5#13068066C211yesmaximal, characteristic, complemented
6#13068065C211yesmaximal, characteristic, complemented
7#13068064C211yesmaximal, characteristic, complemented
8#13068016C211yesmaximal, characteristic, complemented
9#13068015C211yesmaximal, characteristic, complemented
10#13068014C211yesmaximal, characteristic, complemented
11#13068013C211yesmaximal, characteristic, complemented
12#13067389C211yesmaximal, characteristic, complemented
13#13067295C211yesmaximal, characteristic, complemented
14#13067272C211yesmaximal, characteristic, complemented
15C11×#1683C211yesmaximal, characteristic, complemented
16#10623259C2211yescharacteristic
17D11×C4⋊Q8C2211yescharacteristic
18C4×D4×D11C2211yescharacteristic
19C11×#487C2211yescharacteristic, complemented
20C11×#476C2211yescharacteristic
21C11×#474C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23C8×C22⋊D11—21no—
24C2×(C2×D11)⋊C8—21no—
25#10622700C2211yescharacteristic
26#10622697C2211yescharacteristic
27#10622694C2211yescharacteristic, complemented
28#10622691C2211yescharacteristic, complemented
29D4×C11⋊C8C2211yescharacteristic
30#10622621C2211yescharacteristic
31#10622621C2211yescharacteristic
32#10622504—21no—
33#10622494—21no—
34#10622483—21no—
35D11×#106—21no—
36#10622455C2211yescharacteristic
37#10622455C2211yescharacteristic
38#10622450C2211yescharacteristic
39#10622447C2211yescharacteristic
40#10622446C2211yescharacteristic
41D11×C4⋊C8C2211yescharacteristic
42#10622422—21no—
43#10622422—21no—
44#10622407—21no—
45#10622407—21no—
46#10622383—21no—
47D11×#102—21no—
48#10622376—21no—
49#10622374—21no—
50(C22⋊D11)⋊C8—21no—
51D11×C22⋊C8—21no—
52C8×D44C2211yescharacteristic
53#10622298C2211yescharacteristic
54#10622295C2211yescharacteristic, complemented
55C11×#335C2211yescharacteristic, complemented
56C11×#333C2211yescharacteristic, complemented
57C11×#332C2211yescharacteristic, complemented
58#10622185C2211yescharacteristic, complemented
59#10622184C2211yescharacteristic, complemented
60#10622119C2211yescharacteristic, complemented
61#10622119C2211yescharacteristic, complemented
62#10622119C2211yescharacteristic, complemented
63#10622119C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622117C2211yescharacteristic, complemented
66#10622096C2211yescharacteristic, complemented
67C2×Q8×D11—21no—
68C2×D4×D11D411yescharacteristic
69C22×C4×D11—21no—
70C22×C8×C11—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74#66999—21no—
75Q8×Dic11—21no—
76#66997—21no—
77D4×Dic11D411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80C2×#4313—21no—
81C2×C8×D11—21no—
82C2×C8×D11—21no—
83C2×C8×D11—21no—
84#66950—21no—
85#66946D411yescharacteristic
86#66945—21no—
87C4⋊C4×D11—21no—
88C4⋊C4×D11—21no—
89C4⋊C4×D11D411yescharacteristic
90#66943—21no—
91#66941—21no—
92#66941—21no—
93#66940—21no—
94(C22⋊D11)⋊C4—21no—
95C22⋊C4×D11—21no—
96C4×D44C2311yescharacteristic
97C42×D11C2311yescharacteristic
98#66922C2311yescharacteristic
99#66922C2311yescharacteristic
100C11×#107—21no—
101C11×#106—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#103—21no—
106C11×#103—21no—
107C11×#102—21no—
108C11×#102—21no—
109C11×C22⋊C8—21no—
110C4×C8×C11C2311yescharacteristic
111#66899—21no—
112#66899—21no—
113#66896—21no—
114#66896—21no—
115C22⋊(C11⋊C8)—21no—
116#66885—21no—
117#66885—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8D411yescharacteristic
122(C2×D11)⋊C8D411yescharacteristic
123#66882—21no—
124#66882—21no—
125#66881—21no—
126#66881—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8D411yescharacteristic
130Dic11⋊C8D411yescharacteristic
131C8×Dic11—21no—
132#66873—21no—
133#66873—21no—
134#66872—21no—
135#66872—21no—
136#66872—21no—
137#66871—21no—
138#66871—21no—
139#66871—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19393—111nomaximal, Sylow
145C23×D11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×D4×C11C2×D411yescharacteristic
149C22×C4×C11—21no—
150C2×C22⋊D11—21no—
151C22×Dic11—21no—
152Q8×D11—82no—
153D4×D11—22no—
154D4×D11Q1614yes—
155C2×D44C2×D411yescharacteristic
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—41no—
160C2×C4×D11—81no—
161C2×C4×D11—81no—
162C2×C4×D11C2×D411yescharacteristic
163C2×C4×D11C2×D411yescharacteristic
164C2×C4×D11#4111yescharacteristic
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—41no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—81no—
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C22⋊C4—21no—
180C42×C11C2411yescharacteristic
181C22⋊Dic11—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—41no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—41no—
190C4⋊Dic11C2×D411yescharacteristic
191Dic11⋊C4—21no—
192Dic11⋊C4—41no—
193Dic11⋊C4—41no—
194Dic11⋊C4—41no—
195C4×Dic11—41no—
196C4×Dic11C2×D411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—81no—
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205#4313—42no—
206C8×D11—42no—
207C8×D11—81no—
208C8×D11—81no—
209#3230—111no—
210#3077—111no—
211C2×#476—111no—
212#2972—111no—
213#1683—111no—
214#1683—111no—
215#1683—111no—
216#1683D1111yescharacteristic, complemented
217#1675—111no—
218#1675—111no—
219#1675—111no—
220#1675—111no—
221#1571—111no—
222#1548—111no—
223#1542—111no—
224C23×C11—21no—
225C22×D11—21no—
226C22×D11—24no—
227C22×D11—81no—
228C22×D11—81no—
229C22×D11#12111yescharacteristic
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—81no—
233D4×C11—21no—
234D4×C11C2×Q1612yes—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C22⋊D11—24no—
244C2×Dic11—21no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—81no—
248C2×Dic11#12111yescharacteristic
249C2×Dic11#12111yescharacteristic
250C2×Dic11#12111yescharacteristic
251D44—21no—
252D44C2×Q1612yes—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—41no—
256C4×D11—41no—
257C4×D11—41no—
258C4×D11—81no—
259C4×D11—81no—
260C4×D11—82no—
261C4×D11C2×Q1612yes—
262C4×D11#13512yes—
263Dic22—82no—
264Dic22—81no—
265Dic22—81no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11—41no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276#533—111no—
277C2×C4⋊Q8—111no—
278C2×C4×D4—111no—
279#500—111no—
280#500—111no—
281#487—111no—
282#487C2×D1111yescharacteristic, complemented
283#484—221no—
284#484—221no—
285#478—221no—
286#478—221no—
287#477—221no—
288#477—221no—
289#476—111no—
290#476—111no—
291#476—111no—
292#476—111no—
293#476—111no—
294#476—221no—
295#476—221no—
296#476C2×D1111yescharacteristic
297#474—111no—
298#474C2×D1111yescharacteristic
299C8×D4—111no—
300C8×D4—111no—
301C8×D4—111no—
302C8×D4—221no—
303C8×D4—221no—
304C8×D4C2×D1111yescharacteristic
305#431—111no—
306#431—111no—
307#428—221no—
308C2×#106—221no—
309#423—111no—
310C2×C4⋊C8—111no—
311#418—221no—
312C2×#102—221no—
313C2×C22⋊C8—221no—
314C2×C22⋊C8—221no—
315#335—111no—
316#335—111no—
317#335—111no—
318#335C2×D1111yescharacteristic, complemented
319#333—111no—
320#333—111no—
321#333—111no—
322#333—111no—
323#333—111no—
324#333C2×D1111yescharacteristic, complemented
325#332—111no—
326#332C2×D1111yescharacteristic, complemented
327C22×C11—22no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11C2×#12111yescharacteristic
331C2×D11—21no—
332C2×D11—21no—
333C2×D11—22no—
334C2×D11—41no—
335C2×D11—41no—
336C2×D11—84no—
337C2×D11#46712yes—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11C22×Q1611yescharacteristic
343C4×C11C2×#13511yescharacteristic
344C4×C11#57711yescharacteristic
345C4×C11#57711yescharacteristic
346Dic11—21no—
347Dic11—21no—
348Dic11—41no—
349Dic11—81no—
350Dic11—81no—
351Dic11#46712yes—
352C22×Q8—221no—
353C22×D4—111no—
354C23×C4—221no—
355C2×M16—221no—
356C22×C8—21no—
357C22×C8—221no—
358C22×C8—221no—
359C22×C8—221no—
360C22×C8—221no—
361C4⋊Q8—111no—
362C4⋊Q8—111no—
363C4⋊Q8—221no—
364C4⋊Q8—221no—
365C4⋊Q8—221no—
366C4⋊Q8C22×D1111yescharacteristic
367C4⋊Q8C22×D1111yescharacteristic
368#125—221no—
369C22⋊Q8—221no—
370C22⋊Q8—221no—
371C4×Q8—221no—
372C4×Q8—221no—
373C4×D4—111no—
374C4×D4—111no—
375C4×D4—111no—
376C4×D4—221no—
377C4×D4—221no—
378C4×D4C22×D1111yescharacteristic
379#117—221no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C42—111no—
385#107—21no—
386#107—221no—
387#107—221no—
388#107—221no—
389#107—221no—
390#107—221no—
391#106—21no—
392#106—221no—
393#106—221no—
394#106—221no—
395#106—221no—
396#106—221no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404C4⋊C8C22×D1111yescharacteristic
405C4⋊C8C22×D1111yescharacteristic
406C4⋊C8C22×D1111yescharacteristic
407#103—21no—
408#103—21no—
409#103—221no—
410#103—221no—
411#102—21no—
412#102—21no—
413#102—221no—
414#102—221no—
415#102—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419C22⋊C8—21no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C4×C8—111no—
427C4×C8—221no—
428C4×C8C22×D1111yescharacteristic
429C2×C11—42no—
430C2×C11#304211yescharacteristic
431C2×C11C2×#46711yescharacteristic
432C2×C11#306811yescharacteristic
433D11—22no—
434D11—42no—
435C24—221no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—441no—
441C2×Q8—882no—
442C2×D4—114no—
443C2×D4—111no—
444C2×D4—222no—
445C2×D4—221no—
446C2×D4D4×D1111yescharacteristic
447C22×C4—21no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—441no—
456C22×C4—881no—
457C22×C4—881no—
458M16—442no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—81no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—442no—
469C2×C8—881no—
470C2×C8—881no—
471C2×C8—881no—
472C2×C8D4×D1111yescharacteristic
473C2×C8D4×D1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—111no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—441no—
485C4⋊C4—441no—
486C4⋊C4—441no—
487C4⋊C4—441no—
488C4⋊C4D4×D1111yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4—441no—
494C42—111no—
495C42—111no—
496C42—111no—
497C42—441no—
498C42C23×D1111yescharacteristic
499C11#1939311yescharacteristic, complemented, Sylow
500C23—21no—
501C23—111no—
502C23—224no—
503C23—221no—
504C23—881no—
505C23—881no—
506Q8—41no—
507Q8—41no—
508Q8—81no—
509Q8—881no—
510Q8—881no—
511Q8—882no—
512D4—21no—
513D4—112no—
514D4—224no—
515D4—221no—
516D4Q16×D1112yes—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—111no—
523C2×C4—112no—
524C2×C4—112no—
525C2×C4—111no—
526C2×C4—111no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—881no—
536C2×C4—881no—
537C2×C4—882no—
538C2×C4—881no—
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4#41×D1111yescharacteristic
542C8—21no—
543C8—21no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—221no—
548C8—221no—
549C8—441no—
550C8—441no—
551C8—441no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—112no—
556C22—221no—
557C22—221no—
558C22—222no—
559C22—441no—
560C22—441no—
561C22—884no—
562C22D11×#12111yescharacteristic
563C4—21no—
564C4—41no—
565C4—81no—
566C4—81no—
567C4—112no—
568C4—221no—
569C4—221no—
570C4—441no—
571C4—881no—
572C4—881no—
573C4C2×Q16×D1111yescharacteristic
574C4D11×#13511yescharacteristic
575C4#1062330111yescharacteristic
576C4#1062330611yescharacteristic
577C2—42no—
578C2—222no—
579C2—442no—
580C2#1307812611yescharacteristic
581C2D11×#46711yescharacteristic
582C2#1307833911yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1683C2
socleC22×C11C2×#121
prime radicalC2×D4×D11D4
hypercenter#1683D11
hypocenterC11#19393
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1683

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13079763C2semidirect
5. #13068066C2semidirect
6. #13068065C2semidirect
7. #13068064C2semidirect
8. #13068016C2semidirect
9. #13068015C2semidirect
10. #13068014C2semidirect
11. #13068013C2semidirect
12. #13067389C2semidirect
13. #13067295C2semidirect
14. #13067272C2semidirect
15. C11×#1683C2semidirect
19. C11×#487C22semidirect
27. #10622694C22semidirect
28. #10622691C22semidirect
54. #10622295C22semidirect
55. C11×#335C22semidirect
56. C11×#333C22semidirect
57. C11×#332C22semidirect
58. #10622185C22semidirect
59. #10622184C22semidirect
60. #10622119C22semidirect
61. #10622119C22semidirect
62. #10622119C22semidirect
63. #10622119C22semidirect
64. #10622117C22semidirect
65. #10622117C22semidirect
66. #10622096C22semidirect
216. #1683D11semidirect
282. #487C2×D11semidirect
318. #335C2×D11semidirect
324. #333C2×D11semidirect
326. #332C2×D11semidirect
499. C11#19393semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130797632
#130784082
D11×#4762
#130776372
#130680662
#130680652
#130680642
#130680162
#130680152
#130680142
#130680132
#130673892
#130672952
#130672722
C11×#16832
#1939311